arXiv subjects
Publications and source records attributed to Hisao Hayakawa.
The long-time behaviors of the velocity autocorrelation function (VACF) for granular flows based on the optimal velocity fluid model are investigated theoretically. It is found the long-time tail of VACF disappears in a granular flow under the gravity.
The long-time behaviors of the time correlation function $C_η(t)$ of the shear stress for three-dimensional sheared fluids are investigated theoretically. It is found that there are the cross-overs in $C_η(t)$ from $t^{-3/2}$ to $t^{-2}$ for sheared fluids of elastic particles without any thermostat, and from $t^{-3/2}$ to $t^{-5/2}$ for isothermal sheared fluids including granular fluids.
From the molecular dynamics simulation of a system of hard-core disks in which an equilibrium cell is connected with a nonequilibrium cell, it is confirmed that the pressure difference between two cells depends on the direction of the heat flux. From the boundary layer analysis, the velocity distribution function in the boundary layer is obtained. The agreement between the theoretical result and the numerical result is fairly good.
The long-time behavior of the current auto-correlation functions for the velocity, the shear stress and the heat flux is investigated in freely cooling granular gases. It is found that the correlation functions for the velocity and the shear stress have the long-time tails obeying $τ^{-d/2}$, while the correlation function of heat flux decays as $τ^{-(d+2)/2} \exp(-ζ^* τ)$ with the dimensionless cooling rate $ζ^*$, the spatial dimension $d$ and the scaled time $τ$ in terms of the collision frequency. The result of our numerical simulation of the freely cooling granular gases is consistent with the theoretical prediction.
Based on Bhatnagar-Gross-Krook equation coupled with Maxwell equation, we investigate the spatial dependence of a chemical, an electrostatic and an electrochmeical potentials inside a specimen connected with reservoirs. We also confirm that a gap of the chemical potential between at a connection point is negligible.
The rheology of a two-dimensional granular gas under a plane shear is investigated. From the comparison among the discrete element method, the simulation of a set of hydrodynamic equation, and the analytic solution of the steady equation of the hydrodynamic equations, it is confirmed that the fluid equations derived from the kinetic theory give us accurate results even in relatively high density cases.
We study the dynamics of a kink in a one-lane asymmetric simple exclusion process with detachment and attachment of the particle at arbitrary sites. For a system with one site of detachment and attachment we find that the kink is trapped by the site, and the probability distribution of the kink position is described by the overdumped Fokker-Planck equation with a V-shaped potential. Our results can be applied to the motion of a kink in arbitrary number of sites where detachment and attachment take place. When detachment and attachment take place at every site, we confirm that the kink motion obeys the diffusion in a harmonic potential. We compare our results with the Monte Carlo simulation, and check the quantitative validity of our theoretical prediction of the diffusion constant and the potential form.
Collisions and contacts of elastic materials are numerically and theoretically investigated. Using a two-dimensional spring-mass model with defect particles under the free boundary condition, we reproduce the Hertzian contact theory at equilibrium and the quasi-static theory for low speed impacts.
It is demonstrated that $ω^{-4/3}$ law of the power spectrum with the angular frequency $ω$ in dissipative flows is produced by the emission of dispersive waves from the antikink of an congested domain. The analytic theory predicts the spectrum is proportional to $ω^{-2}$ for relatively low frequency and $ω^{-4/3}$ for high frequency.
We study the motion of kinks in a two-lane model of the totally asymmetric simple exclusion process with open boundaries. We analytically study the motion of the kinks by a decoupling approximation. In terms of the decoupling approximation, we find that the positions of the kinks become synchronised,though the difference in the number of particles between lanes remains non-zero when the rate of lane change is asymmetric. The validity of this result is confirmed for small asymmetric cases through the Monte Carlo simulation.
The significance of the recent finding of the velocity distribution function of the steady-state Boltzmann equation under a steady heat current obtained by Kim and Haykawa (J. Phys. Soc. Jpn. {\bf 72}, 1904 (2003)) is discussed. Through the stability analysis, it seems that the steady solution is stable. One of possible applications to the nonequiliburium Knudsen effect in which one cell at equilibrium is connected to another cell under the steady heat conduction is discussed. This solution apparently shows that steady-state thermodynamics proposed by Sasa and Tasaki cannot be used in a naive setup. The preliminary result of our simulation based on molecular-dynamics for nonequilibrium Knudsen effect is also presented to verify the theoretical argument.
The coefficient of normal restitution in an oblique impact is theoretically studied. Using a two-dimensional lattice models for an elastic disk and an elastic wall, we demonstrate that the coefficient of normal restitution can exceed one and has a peak against the incident angle in our simulation. Finally, we explain these phenomena based upon the phenomenological theory of elasticity.
We propose a Langevin model with Coulomb friction. Through the analysis of the corresponding Fokker-Planck equation, we have obtained the steady velocity distribution function under the influence of the external field.
The simulation of granular particles in a quasi two-dimensional container under the vertical vibration as an experimental accessible model for granular gases is performed. The velocity distribution function obeys an exponential-like function during the vibration and deviates from the exponential function in free-cooling states. It is confirmed that this exponential-like distribution function is produced by Coulomb's friction force. A Langevin equation with Coulomb's friction is proposed to describe the motion of such the system.
The velocity distribution function of the steady-state Boltzmann equation for hard-core molecules in the presence of a temperature gradient has been obtained explicitly to second order in density and the temperature gradient. Some thermodynamical quantities are calculated from the velocity distribution function for hard-core molecules and compared with those for Maxwell molecules and the steady-state Bhatnagar-Gross-Krook(BGK) equation. We have found qualitative differences between hard-core molecules and Maxwell molecules in the thermodynamical quantities, and also confirmed that the steady-state BGK equation belongs to the same universality class as Maxwell molecules.
We phenomenologically investigate stick-slip motion of sheared granular layers. Our phenomenology is constructed in the context of nucleation-and-growth of the fluidized area which is triggered by collapsing of stress chains. Based on this picture, we give a simple friction model by introducing the degree of the fluidization. It is found that the present model can successfully reproduce major features of the experimental results reported by Nasuno {\it et al.} (Phys. Rev. E {\bf 58}, 2161 (1998)) with quantitatively good agreement.
We have reviewed recent developments of the theory of the impact for macroscopic elastic materials. This review includes (i) standard theories for the normal impact and the oblique impact, (ii) some typical approaches to simulate impact problems, (iii) and an example of our simulation to clarify the mechanism of anomalous restitution coefficient in an oblique impact in which the restitution coefficient exceeds unity.
The coefficient of normal restitution (COR) in an oblique impact is theoretically studied. Using a two-dimensional lattice models for an elastic disk and an elastic wall, we investigate the dependency of COR on an incident angle and demonstrate that COR can exceed one and have a peak against an incident angle in our simulation. Finally, we explain these phenomena based upon the phenomenological theory of elasticity.